On the proof theory of type two functionals based on primitive recursive operations

This paper is a companion to work of Feferman, Jager, Glas, and Strahm on the proof theory of the type two functionals μ and E1 in the context of Feferman-style applicative theories. In contrast to the previous work, we analyze these two functionals in the context of Schluter's weakened applicative basis PRON which allows for an interpretation in the primitive recursive indices. The proof-theoretic strength of PRON augmented by μ and E1 is measured in terms of the two subsystems of second order arithmetic, Π10-CA and Π11-CA, respectively. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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